The constant-growth dividend discount model (DDM) can be used only when the growth rate is __________
blank
.

Question

BlackTom AI · Accepted Answer

For the constant-growth dividend discount model (DDM) the growth rate g must be strictly less than the required return k (cost of equity), because the model’s price formula is P0 = D1 / (k − g).

1) Relevant knowledge points and concepts
- Constant-growth DDM (Gordon growth model): P0 = D1 / (k − g), where D1 is next period’s dividend, k is the required return (discount rate), and g is the perpetual growth rate of dividends.
- Mathematical and economic requirement: the denominator k − g must be positive for P0 to be finite and economically meaningful.

2) Step-by-step reasoning
- Start with P0 = D1 / (k − g).
- For P0 to be defined and positive, k − g > 0, hence k > g (equivalently g < k).
- If g = k the denominator equals zero, making P0 → ∞ (undefined/infinite), which is not meaningful.
- If g > k the denominator is negative, producing a negative price (or implying divergence), also not meaningful.

3) Calculations / intermediate steps (examples)
- Example with acceptable values: D1 = $1.00, k = 8% (0.08), g = 5% (0.05).
  Denominator = k − g = 0.08 − 0.05 = 0.03.
  P0 = 1.00 / 0.03 = $33.33 (finite and positive).
- If g = k = 0.08:
  Denominator = 0 → P0 undefined (→ ∞).
- If g = 0.10 > k = 0.08:
  Denominator = 0.08 − 0.10 = −0.02 → P0 = 1 / (−0.02) = −$50 (nonsensical).

4) Why the correct answer is correct
Because the formula requires k − g > 0 so the present value converges; therefore g must be less than the required return.

5) Why the other options are incorrect
- “Less than or equal to the required return”: incorrect because equality (g = k) makes the denominator zero and price infinite/undefined.
- “Greater than or equal to the required return” and “Greater than the required return”: both imply k − g ≤ 0, leading to an undefined, infinite, or negative price, which is not economically valid.

6) Conclusion
The correct choice is “less than the required return,” which matches the provided answer.

The constant-growth dividend discount model (DDM) can be used only when the growth rate is __________ blank .单项选择题

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